Many hits for this word are from Australia and about people who share a room/apartment. For example:
オウンキーは1人づつ持たせてもらっているのですが エレベーター操作ができるスワイプキーはシェア。
So, apparently オウンキー
means that you don't have to share the key with someone else living in the same place.
EDIT: in fact, the term seems to have been borrowed from English (1, 2) and not invented by Japanese, so the wasei-eigo tag is probably wrong:
Hi, 1 female needed for living room $180/week only 2 people in the
appartment. [...] All
bills included, Free Internet, Own key, Swimming pool, Gym, Sauna and
Spa!! Very Safe and Secure appartment and the area :)
...
Only 3 people in the room, with your OWN keys. No need to share the keys, so you can get full access 24/7,
(P.S. You should always mention where you found the word and provide some sentences for context; don't assume it's something obvious...)